arXiv 1603.001512016-03-16gr-qchep-th

dS $_{4+2n}$中的引力波存储与四维宇宙学

Gravitational Wave Memory In dS$_{4+2n}$ and 4D Cosmology

Yi-Zen Chu

备注：: 30 pages, 1 figure
DOI：: 10.1088/1361-6382/34/3/035009

摘要：

我们认为，无质量引力子在所有偶数维德西特（dS）时空高于2承认的线性记忆效应所产生的零锥内的传播。假设引力波（GW）是由一个孤立的源产生的，并且只在有限的时间内产生。在这个时间间隔之外，假设GW源的剪应力相对于其能量动量变得可以忽略不计，并且其质量四极矩稳定为静态值。然后，我们证明，横向无痕（TT）GW贡献的扰动的任何dS $_{4+2n}$写在一个共形平坦的形式-源已停止后，主要GW训练已经通过-相当于一个时空常数移位的平坦度规成比例的源的最终和初始质量四极矩的TT部分之间的差异。作为一个副产品，我们提出的解决方案，爱因斯坦的方程线性约德西特背景的所有尺寸大于3。我们指出在四维物质主导宇宙中存在类似但近似的尾诱导线性GW记忆效应。我们在这里的工作是为了改进和扩展arXiv：1504.06337的四维宇宙学结果，这反过来又先于Bieri，Garfinkle和Yau（arXiv：1509.01296）以及Kehagias和Riotto（arXiv：1602.02653）的补充工作。

英文摘要：

We argue that massless gravitons in all even dimensional de Sitter (dS) spacetimes higher than two admit a linear memory effect arising from their propagation inside the null cone. Assume that gravitational waves (GWs) are being generated by an isolated source, and over only a finite period of time. Outside of this time interval, suppose the shear-stress of the GW source becomes negligible relative to its energy-momentum and its mass quadrupole moments settle to static values. We then demonstrate, the transverse-traceless (TT) GW contribution to the perturbation of any dS$_{4+2n}$ written in a conformally flat form -- after the source has ceased and the primary GW train has passed -- amounts to a spacetime constant shift in the flat metric proportional to the difference between the TT parts of the source's final and initial mass quadrupole moments. As a byproduct, we present solutions to Einstein's equations linearized about de Sitter backgrounds of all dimensions greater than three. We then point out there is a similar but approximate tail induced linear GW memory effect in 4D matter dominated universes. Our work here serves to improve upon and extend the 4D cosmological results of arXiv:1504.06337, which in turn preceded complementary work by Bieri, Garfinkle and Yau (arXiv:1509.01296) and by Kehagias and Riotto (arXiv:1602.02653).

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